Answer
A lower estimate for the amount of oil that leaked out is $~~63.2~liters~~$ during this 10 hour time period.
An upper estimate for the amount of oil that leaked out is $~~70.0~liters~~$ during this 10 hour time period.
Work Step by Step
The interval $[0,10]$ is divided into 5 subintervals.
$\Delta t = \frac{b-a}{n} = \frac{10-0}{5} = 2$
Since $r(t)$ is a decreasing function, to find a lower estimate for the amount of oil that leaked out, we can use the right endpoint of each subinterval:
$t_1 = 2$
$t_2 = 4$
$t_3 = 6$
$t_4 = 8$
$t_5 = 10$
We can find a lower estimate for the amount of oil that leaked out:
$\sum_{i=1}^{5} r(t_i)~\Delta t$
$= (7.6+6.8+6.2+5.7+5.3)~(2)$
$= 63.2$
A lower estimate for the amount of oil that leaked out is $~~63.2~liters~~$ during this 10 hour time period.
To find an upper estimate for the amount of oil that leaked out, we can use the left endpoint of each subinterval:
$t_1 = 0$
$t_2 = 2$
$t_3 = 4$
$t_4 = 6$
$t_5 = 8$
We can find an upper estimate for the amount of oil that leaked out:
$\sum_{i=1}^{5} r(t_i)~\Delta t$
$= (8.7+7.6+6.8+6.2+5.7)~(2)$
$= 70.0$
An upper estimate for the amount of oil that leaked out is $~~70.0~liters~~$ during this 10 hour time period.
